Probably. It's random, it could come out as
Or more accurately, Yes, they're secure. They're not truly pseudorandom (Or at least, any good generator, like you'd find in a proper password management application), but follow rules designed to create passwords that aren't random, but very hard to guess.
Password cracking is a known, predictable thing, and you can use that to create passwords that are effective at resisting it. Not dictionary words, long, with symbols, both cases of letters, numbers, so on. Generating a password that would take a modern machine a few million years to crack is not a difficult challenge - because while the people writing the crackers know how the generator works, the people writing the generator know how the crackers work too.
As for lastpass, as far as I know your password container is encrypted and decrypted locally, so very, very little chance of that ever being compromised. Unfortunately, you cannot use lastpass to protect your lastpass container, so you'll have to rely on your own password generating skills to remember that one!